Simplify the following expression: $n = \dfrac{-10y^2 - 40y - 30}{y + 1} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ n =\dfrac{-10(y^2 + 4y + 3)}{y + 1} $ Then we factor the remaining polynomial: $y^2 + {4}y + {3} $ ${1} + {3} = {4}$ ${1} \times {3} = {3}$ $ (y + {1}) (y + {3}) $ This gives us a factored expression: $\dfrac{-10(y + {1}) (y + {3})}{y + 1}$ We can divide the numerator and denominator by $(y - 1)$ on condition that $y \neq -1$ Therefore $n = -10(y + 3); y \neq -1$